Are there any other well recognized/popular opening strategies apart from the greatly overused Australian opening?
Haven’t played for a while, but if I’m in a game with multiple players trying to consolidate Australia/NZ, or I don’t have a good foothold there, I will typically try to sweep across South America as quickly as possible.
It’s not really a very complicated game: try to keep your front lines as small as possible while expanding your territory. Australia just gives you one point of defense to maintain; South America has two, North America (IIRC) has three, so those are usually the easiest places to hold if you can conquer them. Once you’ve amassed armies in Brazil and Central America, you can decide which direction to push into depending on the strength of your opponents.
I’m not sure if Africa or North America is the third easiest. NA is larger than Africa so is harder to initially conquer. Africa has the same number of front-line countries to defend – three – but has more possible way to get attacked. And then of course there’s the fact that NA give 5 bonus armies vs 3.
The Australian plan has the problem of the only available place to expand into is Asia, which is a nightmare. Whether Africa or North America is the next easiest to hold after SA and Australia, it’s important that both are next to South America and neither is next to Australia. I’ll place my opening Army on Peru rather than New Guinea any day.
The only way to win Risk is to not play. 
I much agree with this line of thinking. Also, while I don’t much play Risk with real people, a year or two ago I played a bunch of games on the Risk app, and South America seemed to give the easiest going.
Yeah, I also go for South America first. I usually try to mostly sit in place until I’ve accumulated enough armies, then blitzkrieg through North America. At that point, I only have three front lines, but control of two continents (one of them a big one), which gives me a big edge. And I can also extend my front line out one country to keep anyone else from holding Europe, Africa, or Asia. Once you’re getting seven continental armies per turn and nobody else is getting any (except for maybe that poor schmuck Down Under), it’s only a matter of time.
If I can’t get South America to start with, then I’ll generally go with Madagascar, and try to expand from there to South America. I might end up holding Africa for a turn or two in the process, but that’s not really something I put a high priority on until I’ve established myself in the New World.
Starting in Australia gives you a single point to defend, but it also means you can only expand in one direction as well.
I like to employ the “many-fronts” strategy. I like to start in the center of the map, in the Middle East, Afghanistan, or Russia (or somewhere else in that vicinity). Sure, you’re exposed on all sides, but you can also expand in any direction. When attacked from one direction, simply go the opposite way. Don’t get “married” to a single spot. Be willing to shift your HQ around as needed. Flexibility is an asset.
The thing that makes the Aussie strategy work, usually, is that the most obvious person to deny you is precisely the weakest person on the board: the poor schlub forced to defend a position in Asia. He doesn’t have a continent feeding him extra men for several turns, and he’s going to be nibbled at by both Europe and Africa (as well as North America from time to time), while having to devote large numbers to his SE enemy. If the Aussie gets a set before the Asian does, it’s lights out for the Asian player.
Two extra armies for a few turns and a set isn’t nearly enough to take out Asia. You might be able to knock one player out of Asia, but he’ll probably still have an outpost somewhere else, and there will still be other players in Asia (one of which will have the wherewithal to respond to your weakened state by wiping you out, getting your cards and your continent, and still having whatever territories they started with).
A lot depends on your local metagame. Back when our group played Risk going for Australia early was a death sentence because you would be drawing a huge target on yourself. Every player would target an Australian players territories for their card. Eventually we house ruled a connection from South America to Australia and that re-balances the game considerably. Although out of inertia more than anything I suspect, an early Australia grab was death.
I always found that if, and it is a big if, you can grab North America in the first few turns you’ve probably won. You get so many armies and you’re relatively defensible. Any players in Europe are usually so hard pressed they’re willing to make a deal on reinforcements on Greenland and the UK. So realistically you have two borders and one is in Asia and so rarely a threat.
Adding a connection from Japan to Western USA and/or a connection from Africa to Eastern USA rebalances the game quite a bit. Suddenly there are so many connections nobody ever feels very safe. However, this also makes the game longer as attacks are more tentative and keeping a continent bonus is very difficult.
I’m a big fan of using Madagascar as the homeland and Africa as seat of power. You can easily step foot in South America/Asia/Europe to ruin other people’s plans.
It’s always worked for me, and I’ve been playing the game regularly for, oh, 40 years. <shrug>
I can’t remember the last time I lost on my phone app (playing on the “hard” level with a full field of players–6 players including me), and my strategy is basically to camp out in Australia, build my army while everyone else fights it out, then move into Africa, South America, and up. My strategy may vary slightly if I see a chance to take out an opponent and get his cards, or to keep him from holding a continent for a turn, but I usually just fight the minimal amount of battles in the beginning to mid-point of the game (basically just enough to get cards every turn) and put all my armies on Siam/SE Asia. At some point, when Africa looks vulnerable, I begin to break out and go from there. It’s just too bloody easy and boring of a game on the computer.
IRL, though, it’s a bit trickier, since many Risk players know the Australia strategy. I may bite at it, but if it looks like it’s going to turn into an all-out war for Australia from the first turn, I see if South America might be viable (that’s my second choice for starting position.) Then Africa. But it’s going to be one of those three.
Although, the third poster here has an interesting North America strategy that I kind of want to try since I’m just so bored with the Australia start.